# Extensions 1→N→G→Q→1 with N=C24 and Q=C2×C4

Direct product G=N×Q with N=C24 and Q=C2×C4
dρLabelID
C2×C4×C24192C2xC4xC24192,835

Semidirect products G=N:Q with N=C24 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C241(C2×C4) = C42.16D6φ: C2×C4/C2C22 ⊆ Aut C2496C24:1(C2xC4)192,269
C242(C2×C4) = D24⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:2(C2xC4)192,270
C243(C2×C4) = C23.52D12φ: C2×C4/C2C22 ⊆ Aut C2496C24:3(C2xC4)192,680
C244(C2×C4) = Dic35D8φ: C2×C4/C2C22 ⊆ Aut C2496C24:4(C2xC4)192,431
C245(C2×C4) = S3×C2.D8φ: C2×C4/C2C22 ⊆ Aut C2496C24:5(C2xC4)192,438
C246(C2×C4) = Dic3×D8φ: C2×C4/C2C22 ⊆ Aut C2496C24:6(C2xC4)192,708
C247(C2×C4) = C8⋊(C4×S3)φ: C2×C4/C2C22 ⊆ Aut C2496C24:7(C2xC4)192,420
C248(C2×C4) = D249C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:8(C2xC4)192,428
C249(C2×C4) = SD16⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C2496C24:9(C2xC4)192,723
C2410(C2×C4) = C8⋊S3⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:10(C2xC4)192,440
C2411(C2×C4) = C24⋊C2⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:11(C2xC4)192,448
C2412(C2×C4) = D8⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C2496C24:12(C2xC4)192,711
C2413(C2×C4) = Dic38SD16φ: C2×C4/C2C22 ⊆ Aut C2496C24:13(C2xC4)192,411
C2414(C2×C4) = S3×C4.Q8φ: C2×C4/C2C22 ⊆ Aut C2496C24:14(C2xC4)192,418
C2415(C2×C4) = Dic3×SD16φ: C2×C4/C2C22 ⊆ Aut C2496C24:15(C2xC4)192,720
C2416(C2×C4) = C3×M4(2)⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:16(C2xC4)192,861
C2417(C2×C4) = C3×SD16⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:17(C2xC4)192,873
C2418(C2×C4) = C3×D8⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:18(C2xC4)192,875
C2419(C2×C4) = S3×C8⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24:19(C2xC4)192,263
C2420(C2×C4) = Dic35M4(2)φ: C2×C4/C2C22 ⊆ Aut C2496C24:20(C2xC4)192,266
C2421(C2×C4) = Dic3×M4(2)φ: C2×C4/C2C22 ⊆ Aut C2496C24:21(C2xC4)192,676
C2422(C2×C4) = C4×D24φ: C2×C4/C4C2 ⊆ Aut C2496C24:22(C2xC4)192,251
C2423(C2×C4) = C4×C24⋊C2φ: C2×C4/C4C2 ⊆ Aut C2496C24:23(C2xC4)192,250
C2424(C2×C4) = C12×D8φ: C2×C4/C4C2 ⊆ Aut C2496C24:24(C2xC4)192,870
C2425(C2×C4) = S3×C4×C8φ: C2×C4/C4C2 ⊆ Aut C2496C24:25(C2xC4)192,243
C2426(C2×C4) = C4×C8⋊S3φ: C2×C4/C4C2 ⊆ Aut C2496C24:26(C2xC4)192,246
C2427(C2×C4) = C12×SD16φ: C2×C4/C4C2 ⊆ Aut C2496C24:27(C2xC4)192,871
C2428(C2×C4) = C12×M4(2)φ: C2×C4/C4C2 ⊆ Aut C2496C24:28(C2xC4)192,837
C2429(C2×C4) = C2×C241C4φ: C2×C4/C22C2 ⊆ Aut C24192C24:29(C2xC4)192,664
C2430(C2×C4) = C2×C8⋊Dic3φ: C2×C4/C22C2 ⊆ Aut C24192C24:30(C2xC4)192,663
C2431(C2×C4) = C6×C2.D8φ: C2×C4/C22C2 ⊆ Aut C24192C24:31(C2xC4)192,859
C2432(C2×C4) = Dic3×C2×C8φ: C2×C4/C22C2 ⊆ Aut C24192C24:32(C2xC4)192,657
C2433(C2×C4) = C2×C24⋊C4φ: C2×C4/C22C2 ⊆ Aut C24192C24:33(C2xC4)192,659
C2434(C2×C4) = C6×C4.Q8φ: C2×C4/C22C2 ⊆ Aut C24192C24:34(C2xC4)192,858
C2435(C2×C4) = C6×C8⋊C4φ: C2×C4/C22C2 ⊆ Aut C24192C24:35(C2xC4)192,836

Non-split extensions G=N.Q with N=C24 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C24.1(C2×C4) = M5(2)⋊S3φ: C2×C4/C2C22 ⊆ Aut C24484+C24.1(C2xC4)192,75
C24.2(C2×C4) = C12.4D8φ: C2×C4/C2C22 ⊆ Aut C24964-C24.2(C2xC4)192,76
C24.3(C2×C4) = D242C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.3(C2xC4)192,77
C24.4(C2×C4) = Dic12⋊C4φ: C2×C4/C2C22 ⊆ Aut C24192C24.4(C2xC4)192,275
C24.5(C2×C4) = D244C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.5(C2xC4)192,276
C24.6(C2×C4) = C23.9Dic6φ: C2×C4/C2C22 ⊆ Aut C24484C24.6(C2xC4)192,684
C24.7(C2×C4) = C6.6D16φ: C2×C4/C2C22 ⊆ Aut C24192C24.7(C2xC4)192,48
C24.8(C2×C4) = C6.SD32φ: C2×C4/C2C22 ⊆ Aut C24192C24.8(C2xC4)192,49
C24.9(C2×C4) = C6.D16φ: C2×C4/C2C22 ⊆ Aut C2496C24.9(C2xC4)192,50
C24.10(C2×C4) = C6.Q32φ: C2×C4/C2C22 ⊆ Aut C24192C24.10(C2xC4)192,51
C24.11(C2×C4) = C24.7Q8φ: C2×C4/C2C22 ⊆ Aut C24964C24.11(C2xC4)192,52
C24.12(C2×C4) = Dic12.C4φ: C2×C4/C2C22 ⊆ Aut C24964C24.12(C2xC4)192,56
C24.13(C2×C4) = D81Dic3φ: C2×C4/C2C22 ⊆ Aut C2496C24.13(C2xC4)192,121
C24.14(C2×C4) = C6.5Q32φ: C2×C4/C2C22 ⊆ Aut C24192C24.14(C2xC4)192,123
C24.15(C2×C4) = C24.41D4φ: C2×C4/C2C22 ⊆ Aut C24964C24.15(C2xC4)192,126
C24.16(C2×C4) = Dic35Q16φ: C2×C4/C2C22 ⊆ Aut C24192C24.16(C2xC4)192,432
C24.17(C2×C4) = C8.27(C4×S3)φ: C2×C4/C2C22 ⊆ Aut C2496C24.17(C2xC4)192,439
C24.18(C2×C4) = S3×C8.C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.18(C2xC4)192,451
C24.19(C2×C4) = Dic3×Q16φ: C2×C4/C2C22 ⊆ Aut C24192C24.19(C2xC4)192,740
C24.20(C2×C4) = D85Dic3φ: C2×C4/C2C22 ⊆ Aut C24484C24.20(C2xC4)192,755
C24.21(C2×C4) = D248C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.21(C2xC4)192,47
C24.22(C2×C4) = D24.C4φ: C2×C4/C2C22 ⊆ Aut C24484+C24.22(C2xC4)192,54
C24.23(C2×C4) = C24.8D4φ: C2×C4/C2C22 ⊆ Aut C24964-C24.23(C2xC4)192,55
C24.24(C2×C4) = Dic129C4φ: C2×C4/C2C22 ⊆ Aut C24192C24.24(C2xC4)192,412
C24.25(C2×C4) = D8.Dic3φ: C2×C4/C2C22 ⊆ Aut C24484C24.25(C2xC4)192,122
C24.26(C2×C4) = Q16.Dic3φ: C2×C4/C2C22 ⊆ Aut C24964C24.26(C2xC4)192,124
C24.27(C2×C4) = D82Dic3φ: C2×C4/C2C22 ⊆ Aut C24484C24.27(C2xC4)192,125
C24.28(C2×C4) = M4(2).25D6φ: C2×C4/C2C22 ⊆ Aut C24484C24.28(C2xC4)192,452
C24.29(C2×C4) = D2410C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.29(C2xC4)192,453
C24.30(C2×C4) = Q16⋊Dic3φ: C2×C4/C2C22 ⊆ Aut C24192C24.30(C2xC4)192,743
C24.31(C2×C4) = D84Dic3φ: C2×C4/C2C22 ⊆ Aut C24484C24.31(C2xC4)192,756
C24.32(C2×C4) = C8.Dic6φ: C2×C4/C2C22 ⊆ Aut C24484C24.32(C2xC4)192,46
C24.33(C2×C4) = C24.6Q8φ: C2×C4/C2C22 ⊆ Aut C24484C24.33(C2xC4)192,53
C24.34(C2×C4) = (S3×C8)⋊C4φ: C2×C4/C2C22 ⊆ Aut C2496C24.34(C2xC4)192,419
C24.35(C2×C4) = D247C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.35(C2xC4)192,454
C24.36(C2×C4) = C3×D82C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.36(C2xC4)192,166
C24.37(C2×C4) = C3×M5(2)⋊C2φ: C2×C4/C2C22 ⊆ Aut C24484C24.37(C2xC4)192,167
C24.38(C2×C4) = C3×C8.17D4φ: C2×C4/C2C22 ⊆ Aut C24964C24.38(C2xC4)192,168
C24.39(C2×C4) = C3×M4(2).C4φ: C2×C4/C2C22 ⊆ Aut C24484C24.39(C2xC4)192,863
C24.40(C2×C4) = C3×Q16⋊C4φ: C2×C4/C2C22 ⊆ Aut C24192C24.40(C2xC4)192,874
C24.41(C2×C4) = C3×C8.26D4φ: C2×C4/C2C22 ⊆ Aut C24484C24.41(C2xC4)192,877
C24.42(C2×C4) = C12.15C42φ: C2×C4/C2C22 ⊆ Aut C24484C24.42(C2xC4)192,25
C24.43(C2×C4) = D6.4C42φ: C2×C4/C2C22 ⊆ Aut C2496C24.43(C2xC4)192,267
C24.44(C2×C4) = S3×M5(2)φ: C2×C4/C2C22 ⊆ Aut C24484C24.44(C2xC4)192,465
C24.45(C2×C4) = C16.12D6φ: C2×C4/C2C22 ⊆ Aut C24964C24.45(C2xC4)192,466
C24.46(C2×C4) = C12.7C42φ: C2×C4/C2C22 ⊆ Aut C2496C24.46(C2xC4)192,681
C24.47(C2×C4) = C24.78C23φ: C2×C4/C2C22 ⊆ Aut C24964C24.47(C2xC4)192,699
C24.48(C2×C4) = C2.Dic24φ: C2×C4/C4C2 ⊆ Aut C24192C24.48(C2xC4)192,62
C24.49(C2×C4) = C2.D48φ: C2×C4/C4C2 ⊆ Aut C2496C24.49(C2xC4)192,68
C24.50(C2×C4) = D24.1C4φ: C2×C4/C4C2 ⊆ Aut C24962C24.50(C2xC4)192,69
C24.51(C2×C4) = C4×Dic12φ: C2×C4/C4C2 ⊆ Aut C24192C24.51(C2xC4)192,257
C24.52(C2×C4) = D2411C4φ: C2×C4/C4C2 ⊆ Aut C24482C24.52(C2xC4)192,259
C24.53(C2×C4) = C3×C2.D16φ: C2×C4/C4C2 ⊆ Aut C2496C24.53(C2xC4)192,163
C24.54(C2×C4) = C3×C2.Q32φ: C2×C4/C4C2 ⊆ Aut C24192C24.54(C2xC4)192,164
C24.55(C2×C4) = C3×D8.C4φ: C2×C4/C4C2 ⊆ Aut C24962C24.55(C2xC4)192,165
C24.56(C2×C4) = C12×Q16φ: C2×C4/C4C2 ⊆ Aut C24192C24.56(C2xC4)192,872
C24.57(C2×C4) = S3×C32φ: C2×C4/C4C2 ⊆ Aut C24962C24.57(C2xC4)192,5
C24.58(C2×C4) = C96⋊C2φ: C2×C4/C4C2 ⊆ Aut C24962C24.58(C2xC4)192,6
C24.59(C2×C4) = C4×C3⋊C16φ: C2×C4/C4C2 ⊆ Aut C24192C24.59(C2xC4)192,19
C24.60(C2×C4) = C24.C8φ: C2×C4/C4C2 ⊆ Aut C24192C24.60(C2xC4)192,20
C24.61(C2×C4) = Dic3×C16φ: C2×C4/C4C2 ⊆ Aut C24192C24.61(C2xC4)192,59
C24.62(C2×C4) = C4810C4φ: C2×C4/C4C2 ⊆ Aut C24192C24.62(C2xC4)192,61
C24.63(C2×C4) = D6.C42φ: C2×C4/C4C2 ⊆ Aut C2496C24.63(C2xC4)192,248
C24.64(C2×C4) = S3×C2×C16φ: C2×C4/C4C2 ⊆ Aut C2496C24.64(C2xC4)192,458
C24.65(C2×C4) = C2×D6.C8φ: C2×C4/C4C2 ⊆ Aut C2496C24.65(C2xC4)192,459
C24.66(C2×C4) = D12.4C8φ: C2×C4/C4C2 ⊆ Aut C24962C24.66(C2xC4)192,460
C24.67(C2×C4) = C3×C8○D8φ: C2×C4/C4C2 ⊆ Aut C24482C24.67(C2xC4)192,876
C24.68(C2×C4) = C3×D4○C16φ: C2×C4/C4C2 ⊆ Aut C24962C24.68(C2xC4)192,937
C24.69(C2×C4) = C485C4φ: C2×C4/C22C2 ⊆ Aut C24192C24.69(C2xC4)192,63
C24.70(C2×C4) = C486C4φ: C2×C4/C22C2 ⊆ Aut C24192C24.70(C2xC4)192,64
C24.71(C2×C4) = C48.C4φ: C2×C4/C22C2 ⊆ Aut C24962C24.71(C2xC4)192,65
C24.72(C2×C4) = C24.Q8φ: C2×C4/C22C2 ⊆ Aut C24484C24.72(C2xC4)192,72
C24.73(C2×C4) = C23.27D12φ: C2×C4/C22C2 ⊆ Aut C2496C24.73(C2xC4)192,665
C24.74(C2×C4) = C2×C24.C4φ: C2×C4/C22C2 ⊆ Aut C2496C24.74(C2xC4)192,666
C24.75(C2×C4) = C3×C163C4φ: C2×C4/C22C2 ⊆ Aut C24192C24.75(C2xC4)192,172
C24.76(C2×C4) = C3×C164C4φ: C2×C4/C22C2 ⊆ Aut C24192C24.76(C2xC4)192,173
C24.77(C2×C4) = C3×C8.4Q8φ: C2×C4/C22C2 ⊆ Aut C24962C24.77(C2xC4)192,174
C24.78(C2×C4) = C3×C23.25D4φ: C2×C4/C22C2 ⊆ Aut C2496C24.78(C2xC4)192,860
C24.79(C2×C4) = C6×C8.C4φ: C2×C4/C22C2 ⊆ Aut C2496C24.79(C2xC4)192,862
C24.80(C2×C4) = C2×C3⋊C32φ: C2×C4/C22C2 ⊆ Aut C24192C24.80(C2xC4)192,57
C24.81(C2×C4) = C3⋊M6(2)φ: C2×C4/C22C2 ⊆ Aut C24962C24.81(C2xC4)192,58
C24.82(C2×C4) = C48⋊C4φ: C2×C4/C22C2 ⊆ Aut C24484C24.82(C2xC4)192,71
C24.83(C2×C4) = C22×C3⋊C16φ: C2×C4/C22C2 ⊆ Aut C24192C24.83(C2xC4)192,655
C24.84(C2×C4) = C2×C12.C8φ: C2×C4/C22C2 ⊆ Aut C2496C24.84(C2xC4)192,656
C24.85(C2×C4) = C12.12C42φ: C2×C4/C22C2 ⊆ Aut C2496C24.85(C2xC4)192,660
C24.86(C2×C4) = C3×C8.Q8φ: C2×C4/C22C2 ⊆ Aut C24484C24.86(C2xC4)192,171
C24.87(C2×C4) = C3×C16⋊C4φ: C2×C4/C22C2 ⊆ Aut C24484C24.87(C2xC4)192,153
C24.88(C2×C4) = C3×C82M4(2)φ: C2×C4/C22C2 ⊆ Aut C2496C24.88(C2xC4)192,838
C24.89(C2×C4) = C6×M5(2)φ: C2×C4/C22C2 ⊆ Aut C2496C24.89(C2xC4)192,936
C24.90(C2×C4) = C3×C165C4central extension (φ=1)192C24.90(C2xC4)192,152
C24.91(C2×C4) = C3×M6(2)central extension (φ=1)962C24.91(C2xC4)192,176

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